Turing instability: A spatially uniform steady state can be stable to homogeneous perturbations but unstable to inhomogeneous ones when the inhibitor diffuses faster than the activator (D_v >> D_u). For predator-prey: prey = activator, predator = inhibitor. Cross-diffusion: d₁₂ > 0 means prey flee predators (prey density gradient drives dispersal). Can drive Turing instability even when D_u = D_v. Kinetics: ∂u/∂t = ru(1−u/K) − αuv/(1+βu) + Du∇²u − d₁₂∇²v. Pattern selection: Spots form when predator diffusion dominates; stripes form near the Hopf-Turing co-dimension 2 point.